"A large number of papers have been devoted to the problem of integration of equations of two-dimensional steady nonvertical adiabatic motion of a gas. Most of these papers are based on the application of the hodograph method of S. A. Chaplygin in which the plane of the hodograph of the velocity is taken as the region of variation of the independent variables in the equations of motion; the equations become linear in this plane. The exact integration of these equations is, however, obtained in the form of infinite series containing hypergeometric functions" (p. 1).

"The flow about a conical body of an ideal compressible fluid is considered. Assume that the velocity of the oncoming flow at infinity W is directed along the z-axis. The system of Cartesian coordinates x, y, z with origin at the vertex of the cone O is shown" (p. 1).

"A study is made herein of the irrotational adiabatic motion of a gas in the transition from subsonic to supersonic velocities. A shape of the de Laval nozzle is given, which transforms a homogeneous plane-parallel flow at large subsonic velocity into a supersonic flow without any shockwaves beyond the transition line from the subsonic to the supersonic regions of flow. The method of solution is based on integration near the transition line of the gas equations of motion in the form investigated by S. A. Christianovich" (p. 1).